Suppose that
\(N\)  studies are selected into a meta-analysis for review
from a population of diagnostic studies on the test of interest.
Each study \(i~(i = 1, 2, \dots , N\) )
reports the observed number of
true positives, false negatives, true negatives, and false positives,
denoted by \(n_{11}^i, n_{01}^i, n_{00}^i\) , and \(n_{10}^i\) , respectively,
as formulated in
Table REF .
Let \(n_{+1}^i = n_{11}^i + n_{01}^i\)  be the number of people with the target condition
and
\(n_{+0}^i =n_{00}^i + n_{10}^i\)  the number of people without,
the observed sensitivity and specificity are estimated by
\(\mathrm {\hat{se}}_i = {n_{11}^i}/{n_{+1}^i}\) 
and
\(\mathrm {\hat{sp}}_i = {n_{00}^i}/{n_{+0}^i}\) ,
respectively.
Following [1]},
we define \(\mu _{1i}\)  and \(\mu _{2i}\)  be the logit-transformed
true sensitivity and specificity
of the \(i\) th study.
Reitsma model assumes that \((\mu _{1i}, \mu _{2i})^T\)  is
normally distributed across \(S\)  studies in the population:
\(\binom{\mu _{1i}}{\mu _{2i}}\sim N\left( \binom{\mu _1}{\mu _2}, \Omega  \right)\mathrm {~with~}\Omega  =\begin{pmatrix}\tau _1^2 & \tau _{12} \\\tau _{12} & \tau _2^2\end{pmatrix},\) 
